I always thought it'd be cool to strip Doom down to its core and make it downwardly compatible. Doom's source code has been explored in pretty much every way possible, and ported to everything from handheld consoles and palm PC's all the way up to CGI supercomputers. So why not take advantage of all the major advancements in programming language and downsize it?

I think the most amazing challenge for porting Doom would be to make it compatible with EGA boards. Anyone who'd be able to pull this off, I think, would become a legend in the Doom community by making Doom even more accessible to old-school computer owners. Some things that would change:

No more distance fade
No palette swapping(effects would have to be represented by flashing border or statusbar color)
Viewable size would have to be a bit smaller, possibly in low detail

And other things like that.

Another cool feature would be to port Doom to an online code, like Java or Flash. It'd be great to pop onto a website, click on a Java chat room, meet some opponents, and click to start a match.

The main problem with EGA is it doesn't support 256 colours. Doom in 16 colours is going to really suck.

For really extreme low end graphics, text mode doom is possible; in fact on some Linux distros SDL is linked to aalib (ascii art library) so ports like PrBoom work in the text console with no changes needed... but the "graphics" are terrible :-)

For me, the more interesting challenge would be trying to get the new fangled Doom ports working well on 486s again - let's face it, all the ports struggle on hardware that doom.exe found a breeze.

As to Java-web-Doom, that's going to be impractical except for people with huge bandwidth, sprites and texture mapping mean a lot of graphic frames to be downloaded.